A B C D E F G H We begin this homework by generating some random data. Go to Too

Question

A B C D E F G H

We begin this homework by generating some random data. Go to Tools (Data)Data-AnalysisRandom Number Generation. For “Number of Variables”, enter 1. For “Number of Random Numbers”, enter 40. For “Distribution”, select “Normal”. For “Parameters” enter 240 for mean and 3 for standard deviation. For “Random Seed” enter a random integer between 1 and 32767 (try to choose the number in your mind at random.

We have told Excel we would like a random sample of one random variable, 40 observations, and the observations should be normally distributed with =240 and =3. Under “output options”, select “output range” and enter A1. You are telling Excel to put the observations in column A starting with cell A1. After you click OK you should see 40 numbers in cells A1 through A1000, almost all of which will be between 231 and 249.

Repeat the above instructions, except put another 40 observations from the Normal distribution with a mean of 240 and standard deviation of 3 into columns B, C , and D. Remember to have a different number for “Random Seed” each time. Otherwise, all 4 columns of numbers will be exactly the same! You should finish with a total of 160 observations in cells A1 through D40.

Pretend that each observation is the melting point in degrees Celsius of a sample of a chemical compound. There are 40 random samples of size n=4, one in each row of the spreadsheet. There are 40 chemists working independently of each other, and all of them hae taken a different sample of size n=4 from the population (each scientist knows X is normally distributed and =3, but DOES NOT know .)

All the chemists want to build a 95% confidence interval for using their data. Go to cell F1 and enter =AVERAGE(A1:D1)-(1.96*3/SQRT(4)). This is the left endpoint of the first 95% confidence interval. Put the right endpoint of the 95% confidence interval in cell G1 by going to cell G1 and entering =AVERAGE(A1:D1)+(1.96*3/SQRT(4)).

By copying and pasting cells F1 and G1 (see Homework 0), find all 40 confidence intervals and place them in cells F1 through G40.

Go to cell H1 and enter =(F1<240)*(G1>240). We are asking Excel if the left endpoint of the interval is less than 240 degrees and the right endpoint is greater than 240 degrees. In other words, we are asking if the confidence interval captured . The result is either a 0 (no, it did not) or a 1 (yes, it did). By copying and pasting cell H1 (see Homework 0), find an answer for all 40 confidence intervals and place them in cells H1 through H40.

Go to cell H42 and enter =SUM(H1:H40). You are counting how many of the confidence intervals succeeded in capturing .

1. About how many 95% confidence intervals out of 40 do you expect to capture, on average? How many actually did?

232.9185 233.1619 234.1245 234.783 230.807 236.687 0 239.8256 241.5145 245.2274 239.5602 238.592 244.472 0 238.087 238.029 239.9191 241.7186 236.4984 242.3784 1 242.7773 246.072 238.5914 242.7007 239.5954 245.4754 1 239.6406 239.0627 242.7059 237.2605 236.7274 242.6074 1 244.8431 240.6296 236.4787 238.3725 237.141 243.021 1 243.162 244.7605 235.1099 237.9677 237.31 243.19 1 242.9664 243.4262 240.3412 237.9947 238.2421 244.1221 1 240.9989 241.7138 238.0088 243.472 238.1084 243.9884 1 244.3041 242.4882 243.9219 243.5946 240.6372 246.5172 0 242.7183 241.733 236.0743 239.0294 236.9488 242.8288 1 245.4403 247.6649 237.256 239.203 239.451 245.331 1 235.8803 244.8954 237.3086 238.2943 236.1546 242.0346 1 239.2779 240.1043 237.4481 246.9917 238.0155 243.8955 1 242.599 241.6285 237.1017 240.2045 237.4434 243.3234 1 242.6918 239.6667 239.8033 236.6558 236.7644 242.6444 1 241.9915 242.041 241.5203 241.084 238.7192 244.5992 1 242.3741 236.9678 242.0477 241.7436 237.8433 243.7233 1 240.4604 242.4206 240.0003 239.5403 237.6654 243.5454 1 243.5443 241.3649 242.0033 240.8724 239.0062 244.8862 1 240.0754 237.1873 237.9746 246.9341 237.6028 243.4828 1 242.2019 237.0437 238.9168 244.9216 237.831 243.711 1 238.5814 239.2317 241.0176 244.8592 237.9825 243.8625 1 244.138 240.9607 237.1021 239.3791 237.4549 243.3349 1 237.6331 233.7959 240.1404 242.772 235.6453 241.5253 1 234.7247 239.7294 234.651 234.5739 232.9798 238.8598 0 243.9182 237.5858 244.9304 247.8393 240.6284 246.5084 0 238.3592 238.8745 241.9293 237.3393 236.1856 242.0656 1 241.519 239.2618 239.9055 238.2621 236.7971 242.6771 1 242.0546 239.5437 238.3376 242.8177 237.7484 243.6284 1 239.2492 239.3633 235.1846 241.6365 235.9184 241.7984 1 240.9274 242.6597 242.8406 234.5597 237.3069 243.1869 1 234.6386 239.1627 235.3249 235.8291 233.2988 239.1788 0 238.9087 240.9599 244.6544 240.159 238.2305 244.1105 1 242.5496 241.6256 239.0437 244.8669 239.0814 244.9614 1 239.3535 240.1919 244.8729 239.8569 238.1288 244.0088 1 241.9254 236.4704 242.2897 242.6914 237.9042 243.7842 1 242.3826 245.7267 240.6766 239.1778 239.0509 244.9309 1 240.4481 241.0249 244.1728 238.2185 238.0261 243.9061 1 235.4607 236.5597 236.7916 237.6807 233.6832 239.5632 0

Explanation / Answer

We expected to capture 40 but we actually did 38

234.9239 241.4386 243.7595 232.5736 235.2339 241.1139 1 240.3495 239.6431 243.4819 238.2193 237.4835 243.3635 1 237.0043 237.9941 241.9664 241.0159 236.5552 242.4352 1 239.1873 238.7386 242.134 239.7278 237.0069 242.8869 1 241.7124 241.9653 237.2525 240.628 237.4495 243.3295 1 239.5973 241.6097 234.52 244.9617 237.2322 243.1122 1 238.7085 238.2409 235.7023 239.8454 235.1843 241.0643 1 239.322 241.5265 243.0318 235.6153 236.9339 242.8139 1 240.3306 232.5736 237.8622 234.4868 233.3733 239.2533 0 242.709 245.1974 238.605 240.8762 238.9069 244.7869 1 237.2431 237.8952 241.5685 244.4361 237.3457 243.2257 1 239.6461 235.5878 244.0661 244.4615 238.0004 243.8804 1 238.7354 242.1941 234.7009 237.4126 235.3208 241.2008 1 241.6002 245.3211 239.5033 242.3273 239.248 245.128 1 241.1477 240.041 237.624 243.4595 237.628 243.508 1 243.5936 235.0837 240.7835 240.6618 237.0906 242.9706 1 242.9001 241.7935 243.3141 238.3054 238.6383 244.5183 1 243.8119 242.1172 239.6052 241.823 238.8993 244.7793 1 243.0018 233.7362 236.5592 237.0686 234.6515 240.5315 1 239.8856 234.8811 241.7338 244.505 237.3114 243.1914 1 245.6277 239.1823 243.1652 242.5325 239.6869 245.5669 1 238.1112 235.8248 242.7661 245.1667 237.5272 243.4072 1 241.1613 238.2013 244.7516 243.2788 238.9082 244.7882 1 240.9399 233.5821 240.4307 240.4862 235.9197 241.7997 1 246.5188 234.383 236.6092 235.6576 235.3522 241.2322 1 240.356 237.2276 240.9614 240.7771 236.8905 242.7705 1 245.1769 244.5823 241.0734 241.1324 240.0513 245.9313 0 242.6107 237.9364 237.0254 241.7689 236.8953 242.7753 1 239.1973 239.9971 237.3352 235.5646 235.0836 240.9636 1 240.5797 243.4927 231.8121 237.4828 235.4019 241.2819 1 241.1179 242.2634 239.0688 236.3464 236.7591 242.6391 1 242.2336 236.7254 242.0884 239.965 237.3131 243.1931 1 238.951 244.789 241.519 239.3052 238.201 244.081 1 238.1723 237.1057 239.346 241.8925 236.1891 242.0691 1 237.6221 235.618 244.0834 238.2095 235.9433 241.8233 1 241.9582 240.9512 237.2671 239.4336 236.9625 242.8425 1 240.0965 241.7154 238.7719 237.1504 236.4935 242.3735 1 238.8055 235.0347 241.4083 238.8321 235.5801 241.4601 1 238.2973 237.0321 240.5491 235.4779 234.8991 240.7791 1 235.4693 237.3437 240.4479 237.2315 234.6831 240.5631 1 38

We expected to capture 40 but we actually did 38

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.